A pressure transducer of this type, which enables the measurement of an absolute pressure of a process medium or of a pressure difference, is known from DE 37 05 901 C2. A pressure measuring cell with a housing is disclosed there, in which a measuring membrane is arranged which subdivides a housing interior into a measuring chamber and a reference chamber. The measuring chamber and the reference chamber are each provided with a pressure channel which, when the pressure measuring cell is used in a difference pressure transducer, leads in each case to a separation membrane which separates the measuring chamber and the reference chamber respectively from a measuring medium at which the pressure difference is to be measured between different measuring points. The two chambers are filled with a pressure transfer fluid, a silicone oil for example. In order to generate an electrical measuring signal which changes depending on the applied pressure difference, it is possible for the measuring membrane to carry a pressure sensor which for example is made from silicon and is provided with elongation resistances. By using a facility for evaluating the measuring signal, it is possible to generate and output a measurement value from the electrical measuring signal. Opposite the measuring membrane in the reference chamber is located a piezoelectric element which is provided with electrical connections for control purposes. When energized, this piezoelectric element serves to modulate the hydrostatic pressure in the pressure transfer fluid of the reference chamber. Rapid modulation operations are applied in order that this increase in hydrostatic pressure takes effect in the reference chamber. The equalization of pressure by way of the separation membrane adjacent to the pressure channel can then be ignored. The change in pressure is transmitted to the measuring membrane by means of the pressure transfer fluid. When the amplitude of the pressure modulation is known, the sensitivity of the pressure measuring cell is inferred directly from the amplitude of the corresponding modulation of the measuring signal. Self-monitoring of the pressure measuring cell for malfunctions, particularly of the measuring membrane, is thus enabled during operation and without causing any interruption of the measurement process. The known pressure transducer has the disadvantage, however, that changes in or damage to the separation membrane-cannot be identified.